The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?

$1. \mathrm{\rho Avt}$
$2. \frac{1}{2}\mathrm{\rho Avt}$
$3. 2 \mathrm{\rho Avt}$
$4. \frac{3}{2} \mathrm{\rho Avt}$

Which one of the following is true from the given statements?

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density \(984~\text{kg/m}^3.\) The height of the wine column for normal atmospheric pressure is:
1. \(11.5~\text{m}\)
2. \(10.5~\text{m}\)
3. \(9.00~\text{m}\)
4. \(15.0~\text{m}\)

A hydraulic automobile lift is designed to lift cars with a maximum mass of \(3000\) kg. The area of the cross-section of the piston carrying the load is \(425\) cm². What maximum pressure would the smaller piston have to bear?
1. \(3.12\times10^{5}\) Pa
2. \(1.01\times10^{5}\) Pa
3. \(2.94\times10^{5}\) Pa
4. \(6.92\times10^{5}\) Pa

A \(\mathrm U\text -\)tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with \(10.0~\text{cm}\) of water in one arm and \(12.5~\text{cm}\) of spirit in the other. What is the specific gravity of the spirit?

1. \(0.8\)
2. \(0.3\)
3. \(0.5\)
4. \(0.7\)

Glycerine flows steadily through a horizontal tube of a length of 1.5 m and a radius of 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 × 10^–3 kg s^–1, what is the pressure difference between the two ends of the tube?
(Density of glycerine = $1.3\times {10}^3$ kg m^–3 and viscosity of glycerine = 0.83 Pa-sec).
1. 7.9 × 10⁻² Pa
2. 8.9 × 10⁻³ Pa
3. 9.8 × 10⁻² Pa
4. 6.7 × 10⁻³ Pa

What is the excess pressure inside a bubble of soap solution of radius \(5.00~\text{mm}?\)
(Given that the surface tension of soap solution at the temperature (\(20^{\circ}\text C\)) is \(2.5\times 10^{-2}~\text{N/m}\))
1. \(10~\text{Pa}\) 
2. \(20~\text{Pa}\) 
3. \(1.06\times 10^{5}~\text{Pa}\) 
4. \(15~\text{Pa}\) 

A tank with a square base of an area of 1.0 m² is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 20 cm². The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to a height of 4.0 m. What is the force necessary to keep the door close?

1. 54.88 N
2. 56.0 N
3. 60.0 N
4. 45.5 N

During a blood transfusion, the needle is inserted in a vein where the gauge pressure is \(2000~\text{Pa}.\) At what height must the blood container be placed so that blood may just enter the vein?
(the density of whole blood is \(1.06\times10^{3}~\text{kg/m}^3\))
1. \(0.163~\text m\) 
2. \(0.192~\text m\)
3. \(0.157~\text m\)
4. \(0.754~\text m\)